Are you based in the UK? If so visit your GP and explain to them that you need a letter detailing your condition and what “reasonable adjustments” your employer could make for you. Your employer will need to show that your request to not sit next to that person is unreasonable and with a letter from your GP they will have a very hard time doing that especially with empty desks in the room.
If you have over two years of service in the organisation and your boss does not agree to reasonable adjustments then you could claim that they have forced you out of your job and make a claim for constructive, unfair dismissal
If you have HR explain the condition to them – they should understand the need for making reasonable adjustments.